In statistics and business, a long tail of some distributions of numbers is the portion of the distribution having many occurrences far from the "head" or central part of the distribution. The distribution could involve popularities, random numbers of occurrences of events with various probabilities, etc. The term is often used loosely, with no definition or an arbitrary definition, but precise definitions are possible.

In statistics, the term long-tailed distribution has a narrow technical meaning, and is a subtype of heavy-tailed distribution. Intuitively, a distribution is (right) long-tailed if, for any fixed amount, when a quantity exceeds a high level, it almost certainly exceeds it by at least that amount: large quantities are probably even larger. Note that there is no sense of the "long tail" of a distribution, but only the property of a distribution being long-tailed.

In business, the term long tail is applied to rank-size distributions or rank-frequency distributions (primarily of popularity), which often form power laws and are thus long-tailed distributions in the statistical sense. This is used to describe the retailing strategy of selling many unique items with relatively small quantities sold of each (the "long tail")—usually in addition to selling fewer popular items in large quantities (the "head"). Sometimes an intermediate category is also included, variously called the body, belly, torso, or middle. The specific cutoff of what part of a distribution is the "long tail" is often arbitrary, but in some cases may be specified objectively; see segmentation of rank-size distributions.

The long tail concept has found some ground for application, research, and experimentation. It is a term used in online business, mass media, micro-finance (Grameen Bank, for example), user-driven innovation (Eric von Hippel), knowledge management, and social network mechanisms (e.g. crowdsourcing, crowdcasting, peer-to-peer), economic models, marketing (viral marketing), and IT Security threat hunting within a SOC (Information security operations center).

Frequency distributions with long tails have been studied by statisticians since at least 1946. The term has also been used in the finance and insurance business for many years. The work of Benoît Mandelbrot in the 1950s and later has led to him being referred to as "the father of long tails".

The long tail was popularized by Chris Anderson in an October 2004 Wired magazine article, in which he mentioned Amazon.com, Apple and Yahoo! as examples of businesses applying this strategy. Anderson elaborated the concept in his book The Long Tail: Why the Future of Business Is Selling Less of More.

Anderson cites research published in 2003 by Erik Brynjolfsson, Yu (Jeffrey) Hu, and Michael D. Smith, who first used a log-linear curve on an XY graph to describe the relationship between Amazon.com sales and sales ranking. They showed that the primary value of the internet to consumers comes from releasing new sources of value by providing access to products in the long tail.

The distribution and inventory costs of businesses successfully applying a long tail strategy allow them to realize significant profit out of selling small volumes of hard-to-find items to many customers instead of only selling large volumes of a reduced number of popular items. The total sales of this large number of "non-hit items" is called "the long tail".